Spectral structures of irreducible totally nonnegative matrices (Q2706280)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spectral structures of irreducible totally nonnegative matrices |
scientific article |
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19 March 2001
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totally nonnegative matrices
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spectral structure
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irreducible
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principal rank
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Jordan blocks
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Jordan structures
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Jordan canonical forms
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positive eigenvalues
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Spectral structures of irreducible totally nonnegative matrices (English)
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An \(n\times n\) matrix is called totally positive (TP) (totally nonnegative (TN)) if every minor of \(A\) is positive (nonnegative). The problem is to characterize all possible Jordan canonical forms (Jordan structures) of irreducible totally nonnegative matrices. The authors show that the positive eigenvalues of such matrices have algebraic multiplicity one, and also demonstrate key relationships between the number and sizes of the Jordan blocks corresponding to zero. These notions yield a complete description of all Jordan forms through \(n=7\), as well as numerous general results. Positive eigenvalues of TN matrices are described in Section 3 and Jordan structures of TN matrices are included in Section 4.
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